LMFDB - Elliptic curves over $\Q$ of conductor 1776

The results below are complete, since the LMFDB contains all elliptic curves with conductor at most 500000

Refine search

Conductor	Discriminant	j-invariant	Rank

Bad$\ p$	Curves per isogeny class	Complex multiplication	Torsion

Isogeny class degree	Cyclic isogeny degree	Isogeny class size	Integral points

Analytic order of Ш	$p\ $div$\ $\|Ш\|	Regulator	Reduction	Faltings height

Galois image	Adelic level	Adelic index	Adelic genus

Nonmax$\ \ell$	$abc$ quality	Szpiro ratio	Manin constant

Intrinsic torsion order

			Sort order	Select

Results (22 matches)

Download displayed columns for results to

Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
1776.a1	1776a3	1776.a	1776a	$4$	$4$	$ 2^{4} \cdot 3 \cdot 37 $	$ 2^{10} \cdot 3^{2} \cdot 37 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.47	2B	$1776$	$192$	$3$	$1$	$1$	$3$	$1024$	$0.647042$	$38725206845188/333$	$0.98618$	$5.10804$	$2$	$[0, -1, 0, -7104, 232848]$	$y^2=x^3-x^2-7104x+232848$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.o.1.1, 48.48.0-48.i.1.4, 74.6.0.?, $\ldots$	$[ ]$	$1$
1776.a2	1776a2	1776.a	1776a	$4$	$4$	$ 2^{4} \cdot 3 \cdot 37 $	$ 2^{8} \cdot 3^{4} \cdot 37^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.24.0.7	2Cs	$888$	$192$	$3$	$1$	$1$	$3$	$512$	$0.300468$	$37897488592/110889$	$0.92293$	$3.99664$	$2$	$[0, -1, 0, -444, 3744]$	$y^2=x^3-x^2-444x+3744$	2.6.0.a.1, 4.24.0-4.a.1.1, 24.48.0-24.k.1.1, 148.48.0.?, 296.96.0.?, $\ldots$	$[ ]$	$1$
1776.a3	1776a4	1776.a	1776a	$4$	$4$	$ 2^{4} \cdot 3 \cdot 37 $	$ - 2^{10} \cdot 3^{2} \cdot 37^{4} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.24.0.11	2B	$1776$	$192$	$3$	$1$	$1$	$3$	$1024$	$0.647042$	$-1994709028/16867449$	$0.97056$	$4.15568$	$1$	$[0, -1, 0, -264, 6624]$	$y^2=x^3-x^2-264x+6624$	2.3.0.a.1, 4.24.0-4.d.1.1, 12.48.0-12.e.1.2, 296.48.0.?, 592.96.0.?, $\ldots$	$[ ]$	$1$
1776.a4	1776a1	1776.a	1776a	$4$	$4$	$ 2^{4} \cdot 3 \cdot 37 $	$ 2^{4} \cdot 3^{8} \cdot 37 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.57	2B	$1776$	$192$	$3$	$1$	$1$	$1$	$256$	$-0.046105$	$420616192/242757$	$1.09240$	$3.02452$	$2$	$[0, -1, 0, -39, 18]$	$y^2=x^3-x^2-39x+18$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.o.1.3, 48.48.0-48.i.1.8, 74.6.0.?, $\ldots$	$[ ]$	$1$
1776.b1	1776e1	1776.b	1776e	$2$	$2$	$ 2^{4} \cdot 3 \cdot 37 $	$ 2^{4} \cdot 3^{4} \cdot 37 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$888$	$48$	$0$	$1$	$1$	$1$	$192$	$-0.410509$	$5619712/2997$	$0.96732$	$2.44775$	$2$	$[0, -1, 0, -9, 0]$	$y^2=x^3-x^2-9x$	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.4, 74.6.0.?, 148.24.0.?, $\ldots$	$[ ]$	$1$
1776.b2	1776e2	1776.b	1776e	$2$	$2$	$ 2^{4} \cdot 3 \cdot 37 $	$ - 2^{8} \cdot 3^{2} \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$888$	$48$	$0$	$1$	$1$	$1$	$384$	$-0.063935$	$19600688/12321$	$0.98956$	$2.98528$	$1$	$[0, -1, 0, 36, -36]$	$y^2=x^3-x^2+36x-36$	2.3.0.a.1, 4.6.0.a.1, 24.12.0-4.a.1.1, 148.12.0.?, 296.24.0.?, $\ldots$	$[ ]$	$1$
1776.c1	1776g2	1776.c	1776g	$2$	$3$	$ 2^{4} \cdot 3 \cdot 37 $	$ - 2^{13} \cdot 3 \cdot 37^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$888$	$16$	$0$	$0.139644756$	$1$	$6$	$864$	$0.672521$	$-358667682625/303918$	$1.03817$	$4.66778$	$1$	$[0, -1, 0, -2368, 45184]$	$y^2=x^3-x^2-2368x+45184$	3.4.0.a.1, 12.8.0-3.a.1.2, 888.16.0.?	$[(-24, 296)]$	$1$
1776.c2	1776g1	1776.c	1776g	$2$	$3$	$ 2^{4} \cdot 3 \cdot 37 $	$ - 2^{15} \cdot 3^{3} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$888$	$16$	$0$	$0.418934269$	$1$	$6$	$288$	$0.123214$	$857375/7992$	$0.90609$	$3.30048$	$1$	$[0, -1, 0, 32, 256]$	$y^2=x^3-x^2+32x+256$	3.4.0.a.1, 12.8.0-3.a.1.1, 888.16.0.?	$[(0, 16)]$	$1$
1776.d1	1776b1	1776.d	1776b	$2$	$2$	$ 2^{4} \cdot 3 \cdot 37 $	$ 2^{4} \cdot 3^{2} \cdot 37 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$444$	$12$	$0$	$1$	$1$	$1$	$128$	$-0.511863$	$10061824/333$	$0.84328$	$2.52560$	$1$	$[0, -1, 0, -11, 18]$	$y^2=x^3-x^2-11x+18$	2.3.0.a.1, 12.6.0.c.1, 74.6.0.?, 444.12.0.?	$[ ]$	$1$
1776.d2	1776b2	1776.d	1776b	$2$	$2$	$ 2^{4} \cdot 3 \cdot 37 $	$ - 2^{8} \cdot 3 \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$444$	$12$	$0$	$1$	$1$	$1$	$256$	$-0.165289$	$21296/4107$	$0.90925$	$2.84910$	$1$	$[0, -1, 0, 4, 48]$	$y^2=x^3-x^2+4x+48$	2.3.0.a.1, 6.6.0.a.1, 148.6.0.?, 444.12.0.?	$[ ]$	$1$
1776.e1	1776f1	1776.e	1776f	$1$	$1$	$ 2^{4} \cdot 3 \cdot 37 $	$ - 2^{25} \cdot 3 \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$888$	$2$	$0$	$1$	$1$	$0$	$1248$	$0.515468$	$357911/909312$	$1.04554$	$3.94176$	$1$	$[0, -1, 0, 24, 2928]$	$y^2=x^3-x^2+24x+2928$	888.2.0.?	$[ ]$	$1$
1776.f1	1776k1	1776.f	1776k	$1$	$1$	$ 2^{4} \cdot 3 \cdot 37 $	$ - 2^{35} \cdot 3^{9} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$888$	$2$	$0$	$1$	$1$	$0$	$59616$	$2.311142$	$-670206957616537490521/6109179936768$	$1.09597$	$7.52085$	$1$	$[0, 1, 0, -2917080, -1918643436]$	$y^2=x^3+x^2-2917080x-1918643436$	888.2.0.?	$[ ]$	$1$
1776.g1	1776d1	1776.g	1776d	$1$	$1$	$ 2^{4} \cdot 3 \cdot 37 $	$ - 2^{11} \cdot 3^{5} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$888$	$2$	$0$	$0.066436745$	$1$	$12$	$800$	$0.185303$	$-434163602/8991$	$0.89794$	$3.68194$	$1$	$[0, 1, 0, -200, 1044]$	$y^2=x^3+x^2-200x+1044$	888.2.0.?	$[(10, 12)]$	$1$
1776.h1	1776i1	1776.h	1776i	$1$	$1$	$ 2^{4} \cdot 3 \cdot 37 $	$ - 2^{13} \cdot 3^{11} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$888$	$2$	$0$	$0.133474582$	$1$	$10$	$1056$	$0.739080$	$541343375/13108878$	$0.99284$	$4.29519$	$1$	$[0, 1, 0, 272, -10924]$	$y^2=x^3+x^2+272x-10924$	888.2.0.?	$[(74, 648)]$	$1$
1776.i1	1776h2	1776.i	1776h	$2$	$2$	$ 2^{4} \cdot 3 \cdot 37 $	$ 2^{8} \cdot 3 \cdot 37^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$444$	$12$	$0$	$3.068132738$	$1$	$1$	$192$	$-0.147467$	$9826000/4107$	$0.83989$	$2.89299$	$1$	$[0, 1, 0, -28, -40]$	$y^2=x^3+x^2-28x-40$	2.3.0.a.1, 12.6.0.a.1, 148.6.0.?, 444.12.0.?	$[(-11/2, 39/2)]$	$1$
1776.i2	1776h1	1776.i	1776h	$2$	$2$	$ 2^{4} \cdot 3 \cdot 37 $	$ 2^{4} \cdot 3^{2} \cdot 37 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$444$	$12$	$0$	$1.534066369$	$1$	$3$	$96$	$-0.494040$	$16384000/333$	$0.94193$	$2.59076$	$1$	$[0, 1, 0, -13, 14]$	$y^2=x^3+x^2-13x+14$	2.3.0.a.1, 12.6.0.b.1, 74.6.0.?, 444.12.0.?	$[(-2, 6)]$	$1$
1776.j1	1776c2	1776.j	1776c	$2$	$2$	$ 2^{4} \cdot 3 \cdot 37 $	$ 2^{8} \cdot 3^{6} \cdot 37 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$444$	$12$	$0$	$0.464979531$	$1$	$9$	$384$	$0.133493$	$2885794000/26973$	$0.89518$	$3.65247$	$1$	$[0, 1, 0, -188, 924]$	$y^2=x^3+x^2-188x+924$	2.3.0.a.1, 12.6.0.c.1, 74.6.0.?, 444.12.0.?	$[(-2, 36)]$	$1$
1776.j2	1776c1	1776.j	1776c	$2$	$2$	$ 2^{4} \cdot 3 \cdot 37 $	$ - 2^{4} \cdot 3^{3} \cdot 37^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$444$	$12$	$0$	$0.929959062$	$1$	$3$	$192$	$-0.213081$	$-256000/36963$	$0.99258$	$2.77314$	$1$	$[0, 1, 0, -3, 36]$	$y^2=x^3+x^2-3x+36$	2.3.0.a.1, 6.6.0.a.1, 148.6.0.?, 444.12.0.?	$[(0, 6)]$	$1$
1776.k1	1776j4	1776.k	1776j	$4$	$4$	$ 2^{4} \cdot 3 \cdot 37 $	$ 2^{14} \cdot 3^{12} \cdot 37 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$888$	$48$	$0$	$1$	$1$	$3$	$3456$	$1.113041$	$57588477431113/78653268$	$1.10515$	$5.34636$	$1$	$[0, 1, 0, -12872, 557172]$	$y^2=x^3+x^2-12872x+557172$	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.ba.1.8, 74.6.0.?, 148.24.0.?, $\ldots$	$[ ]$	$1$
1776.k2	1776j3	1776.k	1776j	$4$	$4$	$ 2^{4} \cdot 3 \cdot 37 $	$ 2^{14} \cdot 3^{3} \cdot 37^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$888$	$48$	$0$	$1$	$1$	$1$	$3456$	$1.113041$	$24431916147913/202409388$	$0.99171$	$5.23176$	$2$	$[0, 1, 0, -9672, -366732]$	$y^2=x^3+x^2-9672x-366732$	2.3.0.a.1, 4.12.0-4.c.1.2, 12.24.0-12.h.1.1, 296.24.0.?, 888.48.0.?	$[ ]$	$1$
1776.k3	1776j2	1776.k	1776j	$4$	$4$	$ 2^{4} \cdot 3 \cdot 37 $	$ 2^{16} \cdot 3^{6} \cdot 37^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$444$	$48$	$0$	$1$	$1$	$3$	$1728$	$0.766468$	$29704593673/15968016$	$0.99745$	$4.33465$	$1$	$[0, 1, 0, -1032, 3060]$	$y^2=x^3+x^2-1032x+3060$	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.a.1.2, 148.24.0.?, 444.48.0.?	$[ ]$	$1$
1776.k4	1776j1	1776.k	1776j	$4$	$4$	$ 2^{4} \cdot 3 \cdot 37 $	$ - 2^{20} \cdot 3^{3} \cdot 37 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$888$	$48$	$0$	$1$	$1$	$1$	$864$	$0.419894$	$410172407/255744$	$1.06429$	$3.76228$	$2$	$[0, 1, 0, 248, 500]$	$y^2=x^3+x^2+248x+500$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.1, 24.24.0-24.ba.1.12, $\ldots$	$[ ]$	$1$

Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (22 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search Advanced search options

Results (22 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Refine search